The effects of physiological noise may significantly limit the reproducibility and accuracy of BOLD fMRI. However, physiological noise evidences a complex, undersampled temporal structure and is often non-orthogonal relative to the neuronally-linked BOLD response, which presents a significant challenge for identifying and removing such artifact. This paper presents a multivariate, data-driven method for the characterization and removal of physiological noise in fMRI data, termed PHYCAA (PHYsiological correction using Canonical Autocorrelation Analysis). The method identifies high frequency, autocorrelated physiological noise sources with reproducible spatial structure, using an adaptation of Canonical Correlation Analysis performed in a split-half resampling framework. The technique is able to identify physiological effects with vascular-linked spatial structure, and an intrinsic dimensionality that is task- and subject-dependent. We also demonstrate that increasing dimensionality of such physiological noise is correlated with increasing variability in externally-measured respiratory and cardiac processes. Using PHYCAA as a denoising technique significantly improves simulated signal detection with physiological noise, and real data-driven model prediction and reproducibility, for both block and event-related task designs. This is demonstrated compared to no physiological noise correction, and to the widely used RETROICOR (Glover et al., 2000) physiological denoising algorithm, which uses externally measured cardiac and respiration signals.